# The National Accounts and the Public Sector by Casey B. Mulligan Fall 2010

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1 The National Accounts and the Public Sector by Casey B. Mulligan Fall 2010 Factors of production help interpret the national accounts. The factors are broadly classified as labor or (real) capital. The factors are rented by the organizations featured in the value-added computation: farms, nonfarm businesses, households, nonprofits, etc. Stocks versus Flows A stock refers to the value of an asset at a point in time, while a flow refers to the total value of transactions during an accounting period. 1 A stock is some entity that is accumulated over time by inflows and/or depleted by outflows. Stocks can only be changed via flows. Flows typically are measured over an entire time interval (e.g., investment expenditures for the year), whereas stocks are measured at a particular point in time (e.g., capital in place on December 31 st ). Incomes, expenditures, production, labor, and value-added are all flows. For example, 2004 GDP of \$11.7 trillion means that gross domestic product added up over all of the days of 2004 totaled \$11.7 trillion. Capital can sometimes be confusing as regards to stocks and flows. The term capital sometimes refers to the capital stock, which means (the value of) all of the productive assets in place at a point in time. In this course, capital will always have this meaning. 2 Factors in the Income Accounts Rental payments are tracked in the income accounts. In theory, the income accounts have three types of income: labor income, capital income, and pure profits. GDP = wn + (r+δ)k + (pure profits) where N and K denote the amounts of labor and capital used in production in the country, respectively. wn is the amount of rental income paid to labor, so by definition w is the amount paid per unit labor used. w is often interpreted as the labor rental rate, as it would be if all labor were rented at the same rate. 3 (r+δ)k is gross capital income (a flow). By the same logic, (r+δ) is often interpreted as the gross capital rental rate. Gross refers to gross of capital 1 Please do not confuse the economic concept of stock with some of the various financial industry definitions. In the U.S. financial industry, stock can refer to a claim on a firm s shareholders equity. In the British financial industry, stock can refer to a bond. 2 Capital can also refer to capital services, which are the production services provided by an asset over a period of time. For example, a house is a stock, but the services it provides to its occupant over, say, a month, is a flow. Since this course, and almost all of economics, assumes that a capital stock and the productive services it provides are in a fixed proportion, you cannot go wrong with interpreting capital to mean the capital stock. 3 Of course, labor rents for various rates (otherwise why go to business school?!). Nevertheless, w can (with some cautions noted later) often be interpreted as the average labor rental rate in the economy. 1

2 depreciation; r is the net capital rental rate. This is the same gross referenced in GDP. NDP is net domestic product; it does not include capital depreciation: NDP = wn + rk + (pure profits) For the purposes of this course, we ignore the distinction between factors owned by foreigners and those owned by citizens, which is related to the difference between GDP and GNP. Pure profits are the incomes that accrue to persons over and above what they earn from their contribution of factors of production. In theory, competition would limit pure profits. Later I will argue that pure profits are in fact negligible. In practice, the income accounts do not conform exactly to their theoretical counterpart above, because a particular organization may supply multiple factors of production, and be entitled to pure profits, but receives a combined paycheck. For example, labor union members may earn some pure profits in addition to rental compensation for their labor supplied, but they receive a single wage and salary paycheck. An economist recognizes such a payment as a combined payment. Some of the income claimants in the income accounts are residual claimants, which means that in theory they receive two types of income rental income as a capital owner and pure profits as owner of the organization. For the residual claimants, the national income accounts report only the sum of profits and the capital rental incomes (in one case, the labor rental incomes too). Corporate profits is the residual category for the corporate business sector. Rental income is the residual category for the owner-occupied housing sector. These incomes are usually interpreted as the sum of capital rental and pure profits, but not labor income because the residual claimants typically supply little or no labor by comparison with the capital they supply. For example, the vast majority of shareholders in corporations (weighted by the number of shares they own) do not spend their own time and effort helping with the daily operations of the corporation in which they have ownership. Among those who do, many of them are still supplying little time and effort as compared with capital (Bill Gates is an example). Proprietors' income is the residual category for the noncorporate business sector. In this case, the labor income component of that income cannot be neglected. 4 Usually economists either assume that the factor-components of proprietors income are either all labor income, or accrue in the same proportions as nonproprietors income (i.e., about 2/3 labor income, 1/3 capital income, and 0 pure profit). For the sake of simplicity, these notes assume the later: wn compensation of employees + proprietors income rk rental income + corporate profits + net interest pure profits 0 It can also be argued that indirect business taxes should be included in rk. See Public and Private Sectors below. 4 For example, two lawyers may form a law partnership in which each of them supplies 2500 hours per year worth of work time, and an office with furnishings and supplies worth \$500,000. The rental value of the office and supplies might be \$25,000 or \$30,000 per year (this would be a 5 or 6 percent annual rental rate), but the annual value of the time worked by the two partners might be over \$1,000,000 (this corresponds to an hourly time value of \$200). 2

3 Some countries have income accounts with just three categories: compensation of employees, gross mixed income and gross operating surplus. We interpret gross mixed income as proprietors income and gross operating surplus as the residual (i.e., the categories we interpret above as rk). Factors in the Expenditure Accounts The expenditure accounts track the uses of the economy s output. One of the key entries is investment, which is the connection between the expenditure accounts and factors of production because the capital stock is the accumulation of past investment (a flow) net of depreciation (a flow). Somewhat more complicated notation is needed to keep track of the relation between capital and investment. In particular, capital and investment have time subscripts. t denotes the time period (hereafter, a year ). I t is the total gross investment during the year. There are a couple of ways to time-subscript the capital stock; we let K t denote the stock of capital in place at the end of year t (equivalently, at the beginning of year t+1). We assume that the capital in place at the beginning of year t, which is K t-1 in our notation, is the capital available for production during the year; the K s appearing the income account formulas above would be subscripted by one year prior to the subscripts used for the flows of labor, pure profits, and production. The simplest way to relate investment and capital is through an aggregate perpetual inventory formula. 5 K t = K t-1 - δk t-1 + I t where δ is the fraction of the capital stock that depreciates during the year. In words, the formula says that the capital stock in place at the end of year t is the capital stock in place at the beginning of the year, minus depreciation during the year, plus gross investment occurring during the year. All of these items are measured in dollars (or whatever is the nation s currency), even though some of them are stocks and others are flows. Just like the income and value-added accounts, the expenditure accounts have gross and net versions, where gross refers to gross of depreciation. Gross expenditure is the sum of consumption, net exports, and gross investment. Gross investment is I in our notation. Net expenditure is the sum of consumption, net exports, and net investment. Net investment is gross investment minus depreciation, or (I t -δk t-1 ) in our notation. Private and Public Sectors: Principles and Measurement In principle, factors of production would be treated the same regardless of whether they were located in the private or public sectors. In this case, the total capital stock would be the sum of private and public capital stocks. Private (public) capital would be augmented by private (public) investment, respectively. In practice, public 5 The formula could be (and, in the actual national accounts, is) more complicated in several dimensions: allowing for depreciation rates that vary by asset type, age, and year; allowing for the price of investment goods to vary over time and across assets; etc. We do not consider these complications in our course. 3

5 The National Accounts, the Government Budget, and Government s Control over Resources We have already seen that the same GDP can be calculated in three ways valueadded, income, and expenditure. The government entries in each account are not the same, and none of them are equal to government spending. The value-added account is organized according to the types of organizations doing the production, so the public sector entry in the value-added account is the sum of value-added by public organizations. This includes the value-added of public schools, public hospitals, the military, etc. Public sector value-added is different from government spending for a number of reasons. Public sector value-added is less than government spending to the extent that the government disburses revenues to the private sectors. For example, suppose the government s only spending were on hospitals. Some of its hospital spending went to fund public hospitals, and the rest went to reimbursing patients for the medical bills they incurred at private hospitals. Then public sector value-added would be the value-added of the public hospitals, but government spending would be the sum of the spending by the public hospitals and the government spending on medical reimbursements. The income accounts accumulate income to the factors of production, gross of direct taxes. For example, compensation of employees includes not only the pay that employees take home, but also the taxes that are withheld from their paychecks and taxes that employers pay on their behalf. The income entries do not include transfer payments to individuals. 5

7 Summary These notes discuss the economic interpretation of the national accounts, with special emphasis on the public sector. The factors of production are broadly classified as labor or capital. Value added, income, and expenditure all relate to the factors of production. Government appears in the value-added account because it is one of the institutions that produces. The expenditure accounts show how much capital is accumulated rather than consumed, and government appears in those accounts because both consumption and investment can be directed by the government rather than private persons or businesses. The income accounts feature the rental incomes enjoyed by those owning production factors; government appears there to reconcile those incomes with value-added and national expenditure. 7

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